A wishlist holds things you'd like to get, usually for one occasion, and friends can reserve from it; a collection holds things you recommend, and nobody can reserve from it.
A collection gathers things that belong together, like a room, a hobby or a style, and the things in it are called picks. Side by side:
Dates: a list can have an occasion and a date; a collection has neither.
Who can see it: a collection is either Only me or Everyone; there's no Anyone with the link.
Account: you need one to make a collection.
How do I make a collection?
Once you've signed in, tap your profile picture at the top right, then My collections → New collection.
Tap your profile picture at the top right and choose My collections.
Tap New collection.
Fill in the Collection name, add a description if you like, and choose Who can see it.
Tap Create collection.
To fill it, add things the way you add wishes and pick the collection in Where to add: see "How do I add a wish?". You can also make one there with New collection; like any new collection, it starts as Everyone.
To invite people to help run a collection, see "How do I invite someone to edit my list?". Renaming, covers and deleting work as they do for lists too: see "How do I edit or delete a list?".
Where are my collections?
They're all in the account menu under My collections (tap your profile picture), not under Wishes. The ones set to Everyone also show in the Collections section of your profile.
Why is my collection showing on my profile?
Collections start as Everyone, which puts them on your profile and lets search engines find them. To take one off, open the collection's settings with the sliders icon at the top, tap Who can see it and pick Only me. When you add to a public one, the form says "This collection is public — the item will appear on your page."
For what each option means, see "Who can see my wishlist?". To edit the rest of your profile, see "How do I edit my profile?".
Can friends reserve things from a collection?
No. Friends can copy a pick to their own wishlist with Add to wishlist instead.
Tips
Not ready to show it yet? Start it from My collections, where you can pick Only me before you add anything.
Want something from your collection as a gift? Tap Add to wishlist on it, so friends can reserve it on your list.
Sharing with just a few people? Keep it on Only me and invite them, since anyone can open a collection set to Everyone.